Sources
Census of population Ireland 1926 Vol 3 available online at Central Statistics Ireland website
Census of Population Northern Ireland 1926 County Tables available online at Histpop.org
Commentary:
Based on the county data the increase in population of people from the Free State living in Northern Ireland was slightly greater than 7,000 while there was a minor decline in most Free State Counties of people from Northern Ireland. This suggests that movement from one jurisdiction to the other was minimal but in the direction of Northern Ireland. It is notable that the Northern Irish born population decline of County Armagh was 4,000 greater than the entire population increase of Free State born people. The Census Commissioners of Northern Ireland estimated the migration at 24,000 Census of Population of Northern Ireland: General Report, 1926 (Belfast, 1929), pp. xxv (Histpop) but they admit that this was a best a rough estimate. There is a large difference between 7,000 and 24,000 but the former figure is based on actual figures from both the 1911 census and the 1926 census. Even doubling the figures presented here would only bring the figure to 14,000 suggesting that the 24,000 figure is too high by a factor of 30-70%. If the Northern Irish figure is too high then this suggests greater emigration to the Britain or elsewhere.
Looking at the previous ten years the figures are surprising as the Free State population of Tyrone increased at a greater rate in this period in absolute and percentage than the later 15 year period. In London/Derry county the Free State population had declined 390 in the previous ten years before increasing by 727. As the figures are marginal in both directions it is difficult to form an opinion on this other than to note that there was a general movement (probably economic) from the three counties in future Free State Ulster towards Belfast. However, Antrim Down and Fermanagh had increases that were caused by by factors others than economic.